Carbon has four electrons in its outer electronic shell, which contains one s and three p orbitals. This, however, is the picture for an isolated atom. When the carbon atom is part of a material with a given crystal structure, almost invariably, for energetic reasons imposed by geometric constraints associated with the crystal structure of the material, two or more of these orbitals combine in a hybrid form that is a linear combination of the former. This interesting phenomenon is known as hybridization. When the four orbitals combine in the so-called sp3 hybridization, the hybrid orbitals assemble in the form of a tetrahedron, which is the basic building block of diamond. Conversely, when three orbitals, namely, one s and two p, combine to create hybrid sp2 orbitals, these are now co-planar, pointing to directions that make an angle of 120◦ among themselves. An unexpectedly vast and extremely interesting amount of physical phenomena emerge in materials formed by this form of carbon. Among these we find polyacetylene and graphene, respectively, possessing one- and two-dimensional structures.

Polyacetylene is a polymer presenting a sequence of CH radicals, formed by carbon atoms, each one with three sp2 hybridized orbitals having covalent bonds with two adjacent carbon atoms, thus forming a zig-zag chain (transpolyacetylene). The third hybridized orbital of each carbon atom is covalently bonded to a hydrogen atom. There remains a p-orbital, which does not hybridize, which is occupied by a single electron. Since this orbital admits up to two electrons with opposite spins, the carbon p-electrons in polyacetylene can move all over the chain, being therefore responsible for most of the interesting physics of this polymer. Especially interesting effects derive from the interplay of the carbon p-electrons with the lattice, imparticular with deformations thereof possessing nontrivial topological properties and, for this reason, called topological solitons.

Polyacetylene exhibits remarkable effects, such as the Peierls mechanism, induced by the electron-lattice interaction, by which a gap is generated where otherwise there would be a Fermi surface.